Question

The lengths of two sides of a triangle are shown below:

Side 1: 8x^2-5x-2

Side 2: 7x-x^2+3

The perimeter of the triangle is 4x^3-3x^2+2x-6

Part A: What is the total length of the two sides, 1 and 2, of the triangle? (4 points)

Part B: What is the length of the third side of the triangle? (4 points)

Part C: Do the answers for Part A and Part B show that the polynomials are closed under addition and subtraction? Justify your answer. (2 points)

Answer 1

For Part A: We just add the \(\Large\bf\sf\color{orangered}{\text{first side}}\) and \(\Large\bf\sf \color{royalblue}{\text{second side}}\) together, yes?\[\Large\bf\sf \color{orangered}{8x^2-5x-2}+\color{royalblue}{7x-x^2+3}\]

Answer 2

Remember how to add polynomials like this?
Do we have any `like-terms`?

Answer 3

8x^2 and x^2 are like terms right?

Answer 4

Mmmm k good. So how do they combine? :o

Answer 5

8x^2?

Answer 6

x^2 is the same as 1x^2.

If you think of x^2 as an `apple`.
Then what we're doing is,
we're adding eight `apples` and one `apple` together.

Answer 7

oooo okay so it would be 9x^2 then

Answer 8

Ah my bad, see the subtraction in front of x^2?
We're actually subtracting one apple.
But yes you have the right idea.

Answer 9

So we end up with 7 apples in that case.

Answer 10

Ok good that takes care of the x^2.
\[\Large\bf\sf 7x^2-\color{#DD4747 }{5x}-2+\color{#DD4747 }{7x}+3\]Any other like-terms? :o

Answer 11

5x and 7x

Answer 12

We're subtracting the 5x though, so how do we combine those two terms? :o

Answer 13

7x-5x=2x?

Answer 14

\[\Large\bf\sf 7x^2+\color{#DD4747 }{2x}-2+3\]Ok good.

Answer 15

Any other like termmsssssss? :U

Answer 16

-2 and 3

Answer 17

@zepdrix

Answer 18

so part a answer would be 7x^2+2x+1?

Answer 19

yes.

Answer 20

now how would I do part b?

Answer 21

So we found that the sum of the `first two sides` is:\[\Large\bf\sf \color{#CC0033 }{7x^2+2x+1}\]

They gave us the perimeter of this triangle to be:\[\Large\bf\sf 4x^3-3x^2+2x-6\]The perimeter is the sum of the three sides.
So we can write it like this:\[\Large\bf\sf \color{#CC0033 }{\text{first two sides}}+\color{royalblue}{\text{third side}}\quad=\quad4x^3-3x^2+2x-6\]
\[\Large\bf\sf \color{#CC0033 }{7x^2+2x+1}+\color{royalblue}{\text{third side}}\quad=\quad4x^3-3x^2+2x-6\]

Answer 22

So how do we find the length of the `third side` ? :o

Answer 23

we would have to subtract 7x^2+2x+1 from the perimeter?

Answer 24

good.
So do that, combining like-terms again.

Answer 25

\[\Large\bf\sf \color{royalblue}{\text{third side}}\quad=\quad4x^3-3x^2+2x-6-7x^2-2x-1\]

Answer 26

4x^3 and 7x^2 are like terms?

Answer 27

and -3x^2

Answer 28

@zepdrix

Answer 29

Woops 4x^3 doesn't have any like-terms to combine with.
It has a 3 for the exponent.
No other 3 exponent terms to combine with.

Answer 30

-7x^2 and -3x^2, yes.

Answer 31

so how do I put those together, the subtraction signs are throwing me off

Answer 32

@zepdrix

Answer 33

Ya subtraction and negatives can be kinda tough.

The apples analogy doesn't work as well in this case.

We have -7 apples -_- and we're subtracting 3 apples.

Think of a number line.
You're at -7, and you move 3 to the left.
The puts us at -10 apples.\[\Large\bf\sf -10x^2\]

Answer 34

soo it would be -10x^2

Answer 35

then 2x and -2x are like terms right?

Answer 36

Yes those are like terms.

Answer 37

would they just cancle out to equal just x?

Answer 38

2x and -2x,

You have 2oranges and you subtract 2oranges.

Answer 39

Should leave you with 0x or 0.

Answer 40

would the answer be 4x^3-10x^2+x-7

Answer 41

@zepdrix

Answer 42

zepdrix your latex man *_*

Answer 43

@shamil98 I just downloaded a tex editor.
Trying to figure out how to do this stuff legit D:
Been spoiled with this nice fancy mathjax.

Answer 44

would the answer be 4x^3-10x^2+x-7????????????????

Answer 45

@zepdrix

Answer 46

can someone answer me please??????!!!!!!!!!!!!!!!!

Answer 47

im closing this question and re opening it again